How would I work This Problem out and solve it thank you!
1 answer:
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Answer:
The dimensions of the pool are:
Width: 8.944 feet
Length: 17.888 feet
Step-by-step explanation:
From Geometry, the area of a rectangle (), measured in square feet, is determined by the following equations:
(1)
Where:
- Width, measured in feet.
- Length, measured in feet.
If we know that ,
and
, then we get the following second order polynomial:
(1)
And we solve the expression for :
Then, the dimensions of the pool are, respectively:
and
a. Length of the fence around the field = perimeter of quarter circle = 892.7 ft.
b. The area of the outfield is about 39,584 sq. ft..
<h3>What is the Perimeter of a Quarter Circle?</h3>Perimeter of circle = 2πr
Perimeter of a quarter circle = 2r + 1/4(2πr).
a. The length of the fence around the field = perimeter of the quarter circle fence
= 2r + 1/4(2πr).
r = 250 ft
Plug in the value
The length of the fence around the field = 2(250) + 1/4(2 × π × 250)
= 892.7 ft.
b. Size of the outfield = area of the full field (quarter circle) - area of the infield (cicle)
= 1/4(πR²) - πr²
R = radius of the full field = 250 ft
r = radius of the infield = 110/2 = 55 ft
Plug in the values
Size of the outfield = 1/4(π × 250²) - π × 55²
= 49,087 - 9,503
= 39,584 sq. ft.
Learn more about perimeter of quarter circle on:
